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Research Publications
Chebyshev series
Lagrange’s implicit function theorem
Boundary value problems
Numerical quadrature
General problem of three bodies
Principle of least interaction action
Research Publications
• Back correction methods
• Onboard orbit determination
• Transformations of equations
• Local truncation errors
• Methods with variable step-size
• Minimization with nonlinear
Research Publications
•AI languages and applications
•Fault isolation in real-time expert
•Graphical interfaces for expert
•Windowing systems - X
•Blackboard systems for fault
Current Research Interests
Artificial intelligence
Knowledge-based systems
Machine learning
Real-time expert systems
Computer graphics
Numerical methods
Artificial Intelligence
• Fuzzy logic
• Production systems
• AI languages
• Knowledge representation
• Search techniques
• Reasoning under uncertainty
• Computer vision
Knowledge-based Systems
• Graphics interfaces
• CLIPS (forward chaining)
• Prolog (backward chaining)
• Real-time knowledge-based
• Knowledge acquisition
Machine Learning
• Decision trees
• Markov models
• Bayesian networks
• Neural networks
• Parameter estimation
• Multinomial models
• Data mining applications
Computer Graphics
• Hidden surface elimination
• Quadtrees and octrees
• Linear octrees
• Graphical user interfaces
• Human-computer interaction
• Human factors
Numerical Methods
• Numerical quadrature
• Numerical differentiation
• Numerical solution of ordinary
differential equations
– Stable multistep methods
– Explicit Runge-Kutta methods
• Parallel computation and grid
Research Themes
• Unification / understanding of
problem solving methods
• Developing novel approaches
• Using analogies with other fields
• Focusing on central or core
problem first
• Efficiency / reliability of methods
• Application to real-world problems
Lessons Learned
• Focus on the distinctive characteristics
of techniques or methods, then unify
• Keep things in perspective
• Discuss your ideas with others
• Question every assumption
– Ask why and/or why not
• Save ideas for future study
• Plan ahead
Master’s Thesis
• Ponder
• Be certain it’s what you want to do
• Discuss with faculty with common
interests and expertise in the area
• Identify supervising faculty member
• Do an independent study first
– Fine tune your research interests
– Identify a potential thesis committee
– Develop a thesis proposal with their input
Master’s Thesis (cont’d)
• Once proposal is approved
– Meet with committee to discuss further
your topic and your approach to it
– Meet regularly with your thesis advisor and
committee members while conducting the
– Draft chapters and submit to advisor and
committee as you develop your thesis
– Final completion of thesis and presentation